%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:20:00 EDT 2023

% Result   : Theorem 1.44s 1.83s
% Output   : Proof 1.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.25  % Command    : do_cvc5 %s %d
% 0.24/0.46  % Computer : n029.cluster.edu
% 0.24/0.46  % Model    : x86_64 x86_64
% 0.24/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.46  % Memory   : 8042.1875MB
% 0.24/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.24/0.46  % CPULimit   : 300
% 0.24/0.46  % WCLimit    : 300
% 0.24/0.46  % DateTime   : Sun Aug 27 23:11:41 EDT 2023
% 0.24/0.46  % CPUTime    : 
% 0.31/0.72  %----Proving TF0_NAR, FOF, or CNF
% 1.44/1.83  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.lMdm7EvI9d/cvc5---1.0.5_4164.p...
% 1.44/1.83  ------- get file name : TPTP file name is SWW216+1
% 1.44/1.83  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4164.smt2...
% 1.44/1.83  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.44/1.83  % SZS status Theorem for SWW216+1
% 1.44/1.83  % SZS output start Proof for SWW216+1
% 1.44/1.83  (
% 1.44/1.83  (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal tptp.v_da____) tptp.v_m____) tptp.v_e))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.class_Fields_Olinordered__field tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_5 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (let ((_let_6 (tptp.c_Int_OBit0 _let_5))) (let ((_let_7 (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_6)))) (let ((_let_8 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_9 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_6))) (let ((_let_10 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_11 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_12 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_13 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (let ((_let_14 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_5))) (let ((_let_15 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls))) (let ((_let_16 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls))) (let ((_let_17 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2))))))) (let ((_let_18 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m____))) (let ((_let_19 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal tptp.v_d____) tptp.v_m____))) (let ((_let_20 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_da____ _let_18))) (let ((_let_21 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 tptp.v_m____))) (let ((_let_22 (= _let_20 _let_1))) (let ((_let_23 (not _let_21))) (let ((_let_24 (not _let_3))) (let ((_let_25 (or _let_24 _let_23 _let_22))) (let ((_let_26 (not _let_22))) (let ((_let_27 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Fields_Olinordered__field T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2)))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_23 _let_24 _let_22 (not _let_25)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.v_e tptp.v_da____ tptp.v_m____ tptp.tc_RealDef_Oreal QUANTIFIERS_INST_E_MATCHING ((tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2))))) :args (_let_27))) _let_28 :args (_let_25 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_1 (not _let_20) _let_26))) (ASSUME :args (_let_2)) (ASSUME :args (_let_20)) :args (_let_26 true _let_1 false _let_20)) (ASSUME :args (_let_3)) (ASSUME :args (_let_21)) :args (false false _let_25 true _let_22 false _let_3 false _let_21)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_21 _let_20 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 tptp.v_e) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 tptp.v_da____) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_da____ _let_8) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_19 tptp.v_e) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_d____ _let_18) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 _let_19) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 _let_18) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z) V_w) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_w) V_z))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_z2)) V_z3) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2) V_z3))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 tptp.v_d____) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_d____ _let_8) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 _let_8) (not (= _let_4 _let_8)) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_a) _let_1)))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_ca_2))) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (= V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a_2) V_ca_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_b_2) V_ca_2)) (= V_a_2 V_b_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_y)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2) V_za_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_ly)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_rx) V_ry)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_rx)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_ly) V_ry)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_lx) V_ly)))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_rx) V_ry))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_2 V_ly)) _let_1) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_ly) _let_1))))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_rx)) V_ly))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_ly) V_rx)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_rx) V_ry)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_rx)) V_ry))))) (not (forall ((B_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_d (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_d (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m____))))))) (exists ((B_e $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_e) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_e (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_e (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m____)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2)))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2)))))) _let_17 (forall ((V_a_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2)))))))))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1)))))))))))) (forall ((V_w $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_z V_w)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_z) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_w))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1))))))) (forall ((V_wa_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y_2 _let_1)) (=> (not (= V_za_2 _let_1)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x_2 V_y_2) (tptp.c_Rings_Oinverse__class_Odivide T_a V_wa_2 V_za_2)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2) V_za_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_wa_2) V_y_2)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_a_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_ca_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (and (=> (not _let_2) (= V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2))) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_ca_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> (not _let_2) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2)) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2) V_x_2))) (= V_x_2 _let_1)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) (tptp.c_Groups_Oone__class_Oone T_a)) (= V_a_2 V_b_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (= V_a _let_2))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.c_Groups_Oone__class_Oone T_a))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) V_b) (= V_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= V_b (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) V_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (= V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_m) V_n))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1) (or (= V_a _let_1) (= V_b _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (not (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_b_2) _let_1) (or (= V_a_2 _let_1) (= V_b_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP _let_1 V_b) V_c))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_r)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_a V_r)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_2 V_a_2) (tptp.hAPP _let_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2) V_ca_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_4 tptp.v_da____) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_y) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1) _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_y) _let_1)))) (forall ((V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_b) _let_1)))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z) (= V_z V_w)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (not (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (= V_x_2 V_y_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1))) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_c))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (and (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y_2 _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_d))))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c 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(tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2) V_za_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_za_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x_2) (tptp.hAPP _let_1 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Oone T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1)))))))))))) (forall ((V_a_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_ca_2) V_b_2))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) 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(tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_u) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_v) V_y)) V_a))))))))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_u) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_v) V_y)) V_a))))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 _let_1)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2) _let_1) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x_2)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_f_2 V_g_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_g_2 V_f_2))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Osgn__class_Osgn T_a V_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (= V_a V_b)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ca_2)) (= V_b_2 V_ca_2)))) (forall ((V_ca_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_a_2)) (= V_b_2 V_ca_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (let ((_let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a _let_3)) (=> (not (= V_b _let_3)) (= (tptp.c_Groups_Oplus__class_Oplus T_a _let_2 _let_1) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) _let_2)) _let_1))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (let ((_let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_3)) (=> (not (= V_b _let_3)) (= (tptp.c_Groups_Oplus__class_Oplus T_a _let_2 _let_1) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))) _let_1))))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (= V_a V_b))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1) (= V_a _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_1)) (not (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2) _let_1) (= V_x_2 _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_a)))) (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal _let_4) _let_4) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_b_H)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_xa))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_H) V_b))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_ya) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_ya))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z)))))) (forall ((V_db_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_ca_2 V_db_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_2 V_ca_2) (tptp.hAPP _let_1 V_db_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_2 V_db_2) (tptp.hAPP _let_1 V_ca_2))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c))))) (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_m) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_m)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))) (forall ((V_za_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_wa_2))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_2 V_y_2) (tptp.hAPP _let_1 V_za_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_2 V_za_2) (tptp.hAPP _let_1 V_y_2))) (or (= V_wa_2 V_x_2) (= V_y_2 V_za_2))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_c) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b) V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_e) V_c)))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1) V_w) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2) V_w)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x_2) _let_1) (= V_x_2 _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_y)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_b))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1) (=> (not (= V_a _let_1)) (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (=> (not (= V_a _let_1)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) (tptp.c_Groups_Oone__class_Oone T_a)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_r))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP _let_1 V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP _let_1 V_d))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_m) V_m) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))) (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_m)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) V_m))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x V_y) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_y)))) (forall ((V_S $$unsorted) (V_R $$unsorted)) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_R V_S) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_R) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_S)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2) V_x_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2) V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2) _let_1) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x_2)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))) (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y _let_1)) (=> (not (= V_z _let_1)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_z) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_w) V_y)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_z)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y)) V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y)) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_x) V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) V_y)) V_y))))) (forall ((V_x $$unsorted)) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2) V_x_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2) V_y_2))) (or (not (= V_x_2 _let_1)) (not (= V_y_2 _let_1))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2) V_x_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2) V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_y))))) (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x1) V_y) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_u)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_u) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1)))))))) (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x1) V_y) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_u)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_y) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1)) V_u))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2) V_x_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2) V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (forall ((B_e $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) B_e) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Groups_Oplus__class_Oplus T_a V_y B_e)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y) (= (tptp.hAPP tptp.c_Transcendental_Oln (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x) (tptp.hAPP tptp.c_Transcendental_Oln V_y))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x_2) (tptp.hAPP tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y_2) (= (= (tptp.hAPP tptp.c_Transcendental_Oln V_x_2) (tptp.hAPP tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2)))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x) V_x))) (= (tptp.hAPP tptp.c_Transcendental_Oln _let_8) _let_4) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x_2) (tptp.hAPP tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_Transcendental_Oln V_x)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x) _let_1))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (= (= (tptp.hAPP tptp.c_Transcendental_Oln V_x_2) _let_1) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_Transcendental_Oln V_x)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2))))) (forall ((V_a_2 $$unsorted) (V_wa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))))))))))) (forall ((V_wa_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_2))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_ca_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_ca_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) V_ca_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_wa_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))))))))))) (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal tptp.c_Transcendental_Oln V_x_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (= V_x_2 V_y_2)))) (forall ((V_x_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (=> (tptp.class_Int_Onumber T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) V_z)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_w))) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_w)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 V_y_2)))) (forall ((V_wa_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 _let_2) (not (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b)) _let_1) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b V_a) _let_1) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b V_b) _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c)))))) (forall ((V_wa_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> (not _let_3) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2) V_b_2)) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (= V_ca_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> (not _let_3) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) V_ca_2) V_b_2)) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_wa_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (= V_ca_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) _let_2) (and (=> (not _let_3) (= V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) V_ca_2))) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_a_2 $$unsorted) (V_wa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> (not _let_3) (= V_b_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2))) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_w $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_w))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Odivision__ring T_b)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_b _let_1) (tptp.c_Rings_Oinverse__class_Odivide T_b (tptp.c_Groups_Oone__class_Oone T_b) _let_1))))) (forall ((V_a_2 $$unsorted) (V_wa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))))))))))) (forall ((V_wa_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_2))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_ca_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_ca_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) V_ca_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ca_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_ca_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_wa_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))))))))))) (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal tptp.c_Transcendental_Oln V_x_2 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_x_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.c_Deriv_Oderiv T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_ca_2) V_x_2 V_ca_2))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_Osucc V_k)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_k))))) (forall ((V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 V_a))) (let ((_let_5 (= V_a _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1)))))))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 V_x))) (let ((_let_5 (= V_x _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1)))))))))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_w)))) (forall ((V_z $$unsorted) (V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) V_z) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))) V_z)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x_2) (tptp.hAPP _let_1 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp T_a))) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP _let_1 V_x)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP _let_1 V_x_2) (tptp.hAPP _let_1 V_y_2)) (= V_x_2 V_y_2)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2) V_a_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2) V_b_2)) (or (= V_a_2 V_b_2) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_xa))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_x)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_b))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)) V_b))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_x))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ouminus T_a) (= (tptp.hAPP (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_fun T_b T_a) V_A_2) V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP V_A_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y_2)) (= V_x_2 V_y_2)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_a))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x_2) (tptp.hAPP _let_1 V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.hAPP _let_1 V_z2)) V_z3) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2) V_z3))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z) V_w) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w) V_z))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j)))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_ma_2) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_ma_2) V_n_2) _let_1) (and (= V_ma_2 _let_1) (= V_n_2 _let_1)))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_11 _let_13) (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 V_za_2) (= V_wa_2 V_za_2)))) (forall ((V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 _let_1)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1) V_w) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2) V_w)))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w))) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_z1) (tptp.hAPP _let_1 V_z2))))) (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))) (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_wa_2 V_za_2))) (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 V_za_2))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z))))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))) (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))) (forall ((V_wa_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_wa_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2 V_wa_2) (not (= V_za_2 V_wa_2))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j)))) (forall ((V_x $$unsorted)) (= (tptp.hAPP tptp.c_Transcendental_Oln (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x)) V_x)) (forall ((V_x $$unsorted) (V_u $$unsorted)) (=> (= (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_u) V_x) (= (tptp.hAPP tptp.c_Transcendental_Oln V_x) V_u))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (= (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_y) V_x) (= (tptp.hAPP tptp.c_Transcendental_Oln V_x) V_y))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (not (= (tptp.hAPP (tptp.c_Transcendental_Oexp T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp T_a))) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (tptp.c_Deriv_Oderiv T_a _let_1 V_x_2 (tptp.hAPP _let_1 V_x_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_x)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2) V_x_2) _let_1) (or (= V_x_2 _let_1) (= V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_x $$unsorted) (V_u $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_u) V_u)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_x))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 V_a_2))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x))) (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x))) (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.hAPP (tptp.c_Transcendental_Oexp T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp T_a))) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp T_a))) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))) (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x)))) (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_Transcendental_Oln V_x)) V_x))) (forall ((V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_Transcendental_Oln V_x_2)) V_x_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))) (forall ((V_E_2 $$unsorted) (V_D_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_D_2) (=> (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_E_2) (= V_D_2 V_E_2))))) (forall ((V_Y_2 $$unsorted) (V_X_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_X_2) (=> (= V_X_2 V_Y_2) (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_Y_2))))) (forall ((V_E_2 $$unsorted) (V_D_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_D_2) (=> (= V_D_2 V_E_2) (tptp.c_Deriv_Oderiv T_a V_f_2 V_x_2 V_E_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Groups_Osgn__class_Osgn T_a V_x))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_x))) (let ((_let_5 (= V_x _let_3))) (=> (tptp.class_Groups_Osgn__if T_a) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.hAPP tptp.c_Transcendental_Oln (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oln V_x))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b_H) V_q_H) V_r_H))) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b) V_q) V_r) _let_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_2 _let_1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H))))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b_H) V_q_H) V_r_H))) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b) V_q) V_r) _let_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 _let_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H)))))))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q))))))) (forall ((V_w $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint _let_11) _let_11) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_z)) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_w) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z) V_w)))) (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Osgn__class_Osgn tptp.tc_Int_Oint V_i))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_3 V_i))) (let ((_let_5 (= V_i _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint _let_1)))))))))))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (not (= _let_11 _let_13)) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k) V_k)) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_q))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_q_H)))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_b_H) V_q_H) V_r_H) _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_x) V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_11 _let_13) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_11 _let_11) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (forall ((V_l_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal V_f_2 V_x_2 V_l_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_l_2) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_h $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_h) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_h B_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 B_h))))))))))) (forall ((V_l_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal V_f_2 V_x_2 V_l_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_l_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_h $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_h) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_h B_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP V_f_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 B_h)) (tptp.hAPP V_f_2 V_x_2)))))))))) (forall ((V_za_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.c_Int_Oiszero T_a V_za_2) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls))))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_Opred V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_2 V_v_H_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (and (=> _let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_H_2)) _let_1)))) (forall ((V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_2))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 V_v_H_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls) tptp.c_Int_OPls) (= tptp.c_Int_OPls _let_11) (= _let_12 _let_16) (= _let_16 _let_12) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls V_k) V_k)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls)) (forall ((V_w $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint tptp.c_Int_OPls) V_w) tptp.c_Int_OPls)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls) (forall ((V_x $$unsorted)) (= (tptp.c_Int_Osucc (tptp.c_Int_Opred V_x)) V_x)) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) V_a) V_a))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls _let_11)) (= _let_11 _let_15) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_2 _let_1))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_H tptp.c_Int_OPls))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_v_H))))))))))))) (forall ((V_k $$unsorted) (V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) V_k)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_v_H))) V_k))))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v) V_v_H)))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_Osucc V_v))))))))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) _let_1))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_Osucc V_v))))))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Opred V_k_2) V_l_2))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_y_2)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 tptp.c_Int_OPls)))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_y_2)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 tptp.c_Int_OPls)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_11 _let_15) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (= _let_10 _let_14) (= _let_14 _let_10) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OPls (tptp.c_Int_OBit1 V_l)))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_wa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_wa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 _let_1)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit1 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) V_k))) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k)) (tptp.c_Int_OBit1 (tptp.c_Int_Opred (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)))))) (= (tptp.c_Int_Osucc tptp.c_Int_OPls) _let_5) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) _let_1) _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_x))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (= _let_13 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_5)) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_11 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 _let_5))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y_2)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y_2)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_w))))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2))))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (= (not (= V_ma_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_ma_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))) (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_ma_2)))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2) _let_1) (=> (=> (= V_ma_2 V_n_2) _let_1) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_ma_2) _let_1) _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_ma_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_ma_2 V_n_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_n)) V_k) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n) V_k))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) V_n) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n) V_m))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (not (= V_n_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_n _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_n_2) _let_1) (and (= V_ma_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 _let_1) (= V_n_2 _let_1)))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_k_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2) V_k_2)) (or (= V_ma_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (= (= (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_ma_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_n_2) _let_1) (or (= V_ma_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) _let_1) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1) V_n) _let_1))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2) (= V_ma_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2) (not (= V_ma_2 V_n_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 B_k))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) V_k) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n) V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k))) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) V_m))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_m))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i) V_k) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j) V_k)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j))))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i) V_k) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j) V_l))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_n_2) _let_1) (and (= V_ma_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_n_2)) (and (= V_ma_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_ma_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_ma_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_k_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2) V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i) V_k) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j) V_k))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_ma_2) V_k_2) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2) V_k_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (= V_ma_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2))) (= (= (tptp.hAPP _let_1 V_ma_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_ma_2 V_n_2))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_l_2) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Code__Numeral_Ocode__numeral) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Code__Numeral_Ocode__numeral _let_5)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Code__Numeral_Ocode__numeral tptp.c_Int_OPls)) (forall ((T_a $$unsorted)) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_db_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_db_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x V_db_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_k_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k_2) V_db_2))))))))))) (forall ((V_wa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_wa_2))) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_wa_2))))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Opred (tptp.c_Int_OBit1 V_k)) (tptp.c_Int_OBit0 V_k))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Opred (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit1 (tptp.c_Int_Opred V_k)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit1 V_k))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc (tptp.c_Int_OBit1 V_k)) (tptp.c_Int_OBit0 (tptp.c_Int_Osucc V_k)))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k)) V_l) (tptp.c_Int_OBit0 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k) V_l)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit0 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_k))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)))) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (= V_k_2 tptp.c_Int_OPls))) (forall ((V_l_2 $$unsorted)) (= (= tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l_2)) (= tptp.c_Int_OPls V_l_2))) (= (tptp.c_Int_OBit0 tptp.c_Int_OPls) tptp.c_Int_OPls) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_wa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_wa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 _let_1)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) _let_1) _let_1))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k)) V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k) V_l)) V_l))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k (tptp.c_Int_Osucc V_l))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_n))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_n))))))) (forall ((V_za_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (= V_x_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_y_2 (tptp.hAPP _let_1 V_za_2))) (= (tptp.hAPP _let_1 V_x_2) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_y_2 V_za_2))))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_z) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_12 _let_9) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_11 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_6)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_z) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_10 _let_10) _let_9) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_y))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_r) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_r (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_r_2 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_r_2))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_x _let_1) (= V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 _let_1) V_x))) (forall ((V_D_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2)))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_x_2 _let_3)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 V_x_2) (= V_D_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal _let_2 _let_1))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 _let_3) (= V_D_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_2) _let_1))) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal tptp.c_NthRoot_Osqrt V_x_2 V_D_2)))))))) (forall ((V_k_2 $$unsorted) (V_v_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (not (= V_a_2 V_b_2)) (=> (forall ((B_x $$unsorted)) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal V_v_2 B_x V_k_2)) (= (tptp.hAPP V_v_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a_2 V_b_2) _let_1)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP V_v_2 V_a_2) (tptp.hAPP V_v_2 V_b_2)) _let_1)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 _let_1)))) (forall ((V_y_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y_2)))) (forall ((V_y_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_y_2)))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (= V_x_2 _let_1)))) (= (tptp.hAPP tptp.c_NthRoot_Osqrt _let_8) _let_8) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x)) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_x $$unsorted)) (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x)))) (forall ((V_x $$unsorted)) (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (= V_x_2 V_y_2))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (not (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) _let_1))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 _let_1)))) (forall ((V_y_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y_2)))) (forall ((V_y_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_y_2)))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (=> (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) _let_1) (= V_x _let_1))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) _let_1) (= V_x_2 _let_1)))) (= (tptp.hAPP tptp.c_NthRoot_Osqrt _let_4) _let_4) (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x) V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y) V_y))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_NthRoot_Osqrt V_x))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal _let_1))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_4 _let_7) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 _let_7) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_8 _let_7) (forall ((V_u $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_u) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) V_u))) (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal tptp.c_NthRoot_Osqrt V_x_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 V_u) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_4) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y _let_4) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_3 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_3 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_2) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_2))) V_u))))))))))) (forall ((V_ya $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_xa _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_ya _let_1))))))) (forall ((V_k $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x V_k)) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) V_k))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Power_Opower__class_Opower T_a V_x V_p)) (tptp.c_Power_Opower__class_Opower T_a V_x V_q)) (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Power_Opower__class_Opower T_a V_x V_p) V_q) (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_p) V_q))))) (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_y) V_q) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Power_Opower__class_Opower T_a V_x V_q)) (tptp.c_Power_Opower__class_Opower T_a V_y V_q))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))) (forall ((V_wa_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_wa_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.c_Power_Opower__class_Opower T_a V_a_2 _let_1) _let_2) (and (= V_a_2 _let_2) (not (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a _let_1 _let_2))) (let ((_let_4 (= _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> _let_4 (= _let_3 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_4) (= _let_3 _let_1))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_a)) V_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.c_Power_Opower__class_Opower T_a V_a_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1) (= V_a_2 _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_x) V_x) (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) _let_1) (tptp.c_Power_Opower__class_Opower T_a V_a _let_1))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1) V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_x _let_1) (tptp.c_Power_Opower__class_Opower T_a V_y _let_1)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.c_Power_Opower__class_Opower T_a V_x _let_2) (tptp.c_Power_Opower__class_Opower T_a V_y _let_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y) (= V_x V_y)))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (not (= V_a_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x_2 _let_2) (tptp.c_Power_Opower__class_Opower T_a V_y_2 _let_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))))) (forall ((V_w $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_w))) (=> (and (tptp.class_Groups_Omonoid__mult T_b) (tptp.class_Int_Onumber T_b)) (= (tptp.c_Power_Opower__class_Opower T_b _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b _let_1) _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.c_Power_Opower__class_Opower T_a V_a_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1) (or (= V_a_2 _let_1) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a V_x V_n))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) _let_1))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) _let_1) (tptp.c_Power_Opower__class_Opower T_a V_a _let_1))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x_2 _let_2) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y_2 _let_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 _let_1))) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_2)) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) V_x) _let_2))))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_n))) (forall ((V_x $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_u _let_1)) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_x _let_1) (tptp.c_Power_Opower__class_Opower T_a V_y _let_1)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x _let_1) (tptp.c_Power_Opower__class_Opower T_a V_y _let_1)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x_2 _let_2) (tptp.c_Power_Opower__class_Opower T_a V_y_2 _let_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x _let_1) (tptp.c_Power_Opower__class_Opower T_a V_y _let_1)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x_2 _let_2) (tptp.c_Power_Opower__class_Opower T_a V_y_2 _let_2))) (or (not (= V_x_2 _let_1)) (not (= V_y_2 _let_1)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) _let_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Power_Opower__class_Opower T_a V_x _let_2) (tptp.c_Power_Opower__class_Opower T_a V_y _let_2)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a _let_1)) V_x)) V_y))))))) (forall ((V_k $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_k)) _let_1) (= V_a _let_1))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (= (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) V_y)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x))) (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1)))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1)))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_c) _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_b V_d) _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_a _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_b _let_1))) (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_c _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_d _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1))) V_x) (= V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (= (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1))) V_y) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((V_ya $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_xa _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_ya _let_1))))) (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt _let_2) _let_1) _let_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1)))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt V_x)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (= (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) _let_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_2) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_2)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) V_x)) V_y)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n))))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat V_i V_m) (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat V_i V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat V_x_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_x_2) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x V_n))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x V_y)) (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x V_z)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x V_y) V_z) (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_y) V_z)))) (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat V_x_2 V_n_2)) (or (= V_n_2 _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_x_2))))) (forall ((V_wa_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_wa_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat V_x_2 _let_2)) (or (= _let_2 _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_x_2)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a _let_1)) (not (= (tptp.c_Power_Opower__class_Opower T_a V_a V_n) _let_1)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b) V_n) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Power_Opower__class_Opower T_a V_b V_n))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_1) V_a) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a _let_1 V_n) _let_1)))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m) V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_m) V_n)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_n)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n)))))) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.c_Power_Opower__class_Opower T_a V_a_2 V_n_2) _let_1) (and (= V_a_2 _let_1) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))) (forall ((V_n_2 $$unsorted) (V_ma_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) (= (= (tptp.c_Power_Opower__class_Opower T_a V_a_2 V_ma_2) (tptp.c_Power_Opower__class_Opower T_a V_a_2 V_n_2)) (= V_ma_2 V_n_2))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Power_Opower__class_Opower T_a V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_m)) (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_a) V_n))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_n))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1)))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a _let_1 V_n))) (let ((_let_3 (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_n) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_n)) (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_b_2 V_x_2) (tptp.c_Power_Opower__class_Opower T_a V_b_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_m) (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_a V_N)))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_a V_N)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) _let_1) _let_1)))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_N) (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.c_Power_Opower__class_Opower T_a V_a V_n) (tptp.c_Power_Opower__class_Opower T_a V_b V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_a V_b)))))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_N) (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_b_2 V_x_2) (tptp.c_Power_Opower__class_Opower T_a V_b_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2 V_y_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_m) (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))))) (forall ((V_z $$unsorted)) (= (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.hAPP tptp.c_Transcendental_Oarctan V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) (tptp.hAPP tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_2 (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1)))))))))))) (= (tptp.hAPP tptp.c_Transcendental_Oarctan _let_4) _let_4) (forall ((V_x $$unsorted)) (= (tptp.hAPP tptp.c_Transcendental_Oarctan (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oarctan V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oarctan V_x) (tptp.hAPP tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_Transcendental_Oarctan V_x) (tptp.hAPP tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_x_2 $$unsorted)) (tptp.c_Deriv_Oderiv tptp.tc_RealDef_Oreal tptp.c_Transcendental_Oarctan V_x_2 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_1))))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_y $$unsorted) (V_u $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) _let_3) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y) _let_3) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_x _let_2) (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal V_y _let_2))) V_u))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_n)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n)) (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_n)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Power_Opower__class_Opower T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_n)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Power_Opower__class_Opower T_a V_a V_n))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y))) (= V_x _let_1))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_y)) V_x) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_y) V_x)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring__abs T_a) (=> (and (or (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1)) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_a) V_b)) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Oabs__if T_a) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))) (=> (not _let_2) (= _let_1 V_a))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_x) V_y) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a _let_1) _let_1)))) (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (let ((_let_2 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a _let_2) _let_1) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a V_c) V_d)))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_1) (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ouminus T_1) (tptp.class_Groups_Ouminus (tptp.tc_fun T_2 T_1)))) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint) (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring tptp.tc_Int_Oint) (tptp.class_Orderings_Oord tptp.tc_Int_Oint) (tptp.class_Groups_Ouminus tptp.tc_Int_Oint) (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint) (tptp.class_Groups_Oabs__if tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint) (tptp.class_Power_Opower tptp.tc_Int_Oint) (tptp.class_Groups_Ozero tptp.tc_Int_Oint) (tptp.class_Rings_Oring tptp.tc_Int_Oint) (tptp.class_Rings_Oidom tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Groups_Oone tptp.tc_Int_Oint) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat) (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Power_Opower tptp.tc_Nat_Onat) (tptp.class_Groups_Ozero tptp.tc_Nat_Onat) (tptp.class_Int_Onumber tptp.tc_Nat_Onat) (tptp.class_Groups_Oone tptp.tc_Nat_Onat) (tptp.class_Lattices_Oboolean__algebra tptp.tc_HOL_Obool) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Groups_Ouminus tptp.tc_HOL_Obool) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal) _let_3 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ouminus tptp.tc_RealDef_Oreal) (tptp.class_Groups_Osgn__if tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oabs__if tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal) (tptp.class_Power_Opower tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal) (tptp.class_SEQ_Obanach tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ouminus tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex) (tptp.class_SEQ_Obanach tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semidom tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ocomm__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ozero__neq__one tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Opreorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Olinorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Omonoid__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Omonoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring__1 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring__0 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Omult__zero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Oorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Oord tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Power_Opower tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ozero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Int_Onumber tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oone tptp.tc_Code__Numeral_Ocode__numeral) _let_2 true)))))))))))))))))))))))))))))))
% 1.66/1.84  )
% 1.66/1.84  % SZS output end Proof for SWW216+1
% 1.66/1.84  % cvc5---1.0.5 exiting
% 1.66/1.84  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------